Finite-difference scheme for two-scale homogenized equations of one-dimensional motion of a thermoviscoelastic Voigt-type body

The Bakhvalov–Eglit two-scale homogenized equations are used to describe the motion of layered periodic compressible media with rapidly oscillating data. A new finite-difference scheme for a system of such equations is proposed and analyzed in the case of a thermoviscoelastic Voigt-type body. A priori estimates of solutions are derived for nonsmooth data. The existence and uniqueness of discrete solutions are established. A theorem is proved on the convergence of a subsequence of discrete solutions to a weak solution of the problem under study. Simultaneously, a new theorem on the existence of global weak solutions is deduced.